Calculus/Calc 1

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Expert: Alon Mandes - 10/20/2009


Question
I'm having trouble finding the derivative of

g(x)= (1+4x)^5(3+x-x^2)^8   and is this problem the same way? (x^4-1)^3(x^3+1)^4

Thanks

Answer
We will follow the rule : [fg]'=f'g+fg'. In our case : f=(1+4x)^5 & g=(3+x-x^2)^8.Therefore,
[(1+4x)^5(3+x-x^2)^8]'=[(1+4x)^5]'[(3+x-x^2)^8]+[(1+4x)^5][(3+x-x^2)^8]'=
[5*4*(1+4x)^4][(3+x-x^2)^8]+[(1+4x)^5][8*(1-2x)*(3+x-x^2)^7]=
[20(1+4x)^4][(3+x-x^2)^8]+[(1+4x)^5][8(1-2x)(3+x-x^2)^7]=
{ [(1+4x)^4][(3+x-x^2)^7] } * { 20(3+x-x^2) + 8(1+4x) } .
Note that :
[ (a+bx)^n ]'=nb(a+bx)^(n-1) & [ (a+bx-cx^2)^n ]'=n(b-cx)(a+bx-cx^2)^(n-1) .

Alon.

Calculus

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Alon Mandes

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Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

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1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

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Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

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M.A in Mathematics & Bs.c in Electronics.

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